Current inversion method of steel tape armored multi-core cable

Abstract

The invention discloses a current inversion method for a steel tape armored multi-core cable, and the method comprises the steps: S1, setting a plurality of measurement points at a to-be-measured part of a to-be-measured multi-core cable, building a polar coordinate system with the geometric center of the to-be-measured multi-core cable as an original point, and constructing a position coefficient matrix, a conductor current matrix, and an attenuation coefficient matrix; s2, assigning an initial value to the unknown variable, and calculating to obtain an initial conductor current matrix and an initial attenuation coefficient matrix; s3, searching a local optimal solution of the attenuation coefficient matrix through a random optimization method; s4, constructing a linear equation set taking the conductor current matrix as an unknown variable to solve the conductor current matrix; and S5, after the sampling value of the magnetic induction intensity component is updated, solving the linear equation set, and calculating to obtain the current value of each conductor of the current cable. According to the method, on the basis of the time-invariant characteristic of the magnetization curve, the undetermined coefficient of the approximation function is solved by using the stochastic optimization algorithm, the nonlinear attenuation coefficient of the steel tape armoring of the target cable is solved, the influence of the steel tape armoring on the current inversion result is corrected, and the measurement efficiency and precision can be improved.

Description

Technical Field

[0001] The invention relates to a cable current measurement technology, in particular to a current inversion method for a steel belt armored multi-core cable. Background Art

[0002] In large urban distribution networks, power cables are the core equipment for power transmission and distribution. When a large amount of power needs to be transmitted, in order to reduce the impact of the skin effect, power cables in urban distribution networks are mostly implemented with multi-core cables. Cable load current is the core indicator for evaluating cable operating performance, and it is also the core indicator for monitoring the operating status of distribution networks. Accurately measuring the current of multi-core cables provides perfect data support for power grid operation monitoring, which has great practical significance for ensuring the safe operation of cables and supporting the operating status evaluation and planning decision-making of distribution networks.

[0003] However, since the conductors of multi-core cables are enclosed in a multi-layer protective structure, direct current measurement of the conductors will damage the cable structure, which is contrary to the requirements of safe operation. In addition, the external magnetic flux of a multi-core cable is a synthetic magnetic flux generated by the currents of each conductor, which makes it difficult to independently decouple and measure the currents of each conductor using traditional non-invasive measurement equipment (such as current transformers and Rogowski coils). At present, a more effective solution is to reconstruct the current distribution of multi-core cables through spatial magnetic field inversion technology. The specific implementation method is to arrange a magnetic field sensor array on the outer surface of the cable, measure the local magnetic field distribution, and establish and solve a nonlinear set of equations containing the conductor position and current based on the field source position relationship, thereby realizing non-invasive measurement of the current of multi-core cables.

[0004] It is worth noting that most medium-voltage power cables use armored structures, especially ferromagnetic steel belt armor, to enhance the cable's protection and anti-interference performance. Under the action of the magnetic field, the steel belt will be magnetized and generate an additional magnetic field, which will cause the measured magnetic field to attenuate relative to the magnetic field without armor. If the coefficient matrix representing the field source relationship is not corrected, this attenuation will cause errors in the inversion calculation, thereby affecting the accuracy of the current measurement. To solve this problem, the existing method is to model the cable structure including the steel belt armor and the core conductor through finite element calculation, and solve the corrected position coefficient matrix. However, this method has the following two main disadvantages: First, finite element calculation requires a large amount of grid division and the solution of differential equations in each grid unit, which not only increases the amount of calculation and time consumption, but may also lead to the complexity, power consumption and cost increase of the current measurement equipment, affecting the real-time measurement; secondly, the magnetization curve of ferromagnetic materials has nonlinear characteristics, and finite element calculation must also require that this information must be mastered in advance. However, due to differences in raw materials and processes among different manufacturers, the magnetization curve of the steel strip armor of the power cable actually used may be inconsistent with the curve used for calculation. The calculation error will limit the suppression effect on the influence of ferromagnetic materials, thereby making the current measurement accuracy of multi-core cables low. Summary of the invention

[0005] The purpose of the present invention is to solve the problems of poor real-time performance and low current measurement accuracy in the existing process of reconstructing the current distribution of a multi-core cable by means of spatial magnetic field inversion technology, in which a coefficient matrix representing the field source relationship is corrected by means of finite element calculation. A current inversion method for a steel-belt armored multi-core cable is provided. The method is based on the time-invariant characteristic of a magnetization curve, utilizes a random optimization algorithm to solve the unknown coefficients of an approximation function, solves the nonlinear attenuation coefficient of the steel-belt armor of the target cable, corrects the influence of the steel-belt armor on the current inversion result, and can improve the measurement efficiency and accuracy.

[0006] The purpose of the present invention is mainly achieved through the following technical solutions:

[0007] A current inversion method for a steel tape armored multi-core cable comprises the following steps:

[0008] Step S1, setting a plurality of measurement points uniformly distributed along the circumference of the outer surface of the to-be-tested part at the to-be-tested part of the to-be-tested multi-core cable, establishing a polar coordinate system with the geometric center of the to-be-tested multi-core cable as the origin, constructing a position coefficient matrix according to the magnetic field measurement values ​​measured by the magnetic field sensor at the measuring points generated by the conductors in the to-be-tested multi-core cable; constructing a conductor current matrix according to the current calculated according to the magnetic field measurement values ​​at different times to obtain the current values ​​of each conductor of the multi-core cable at different times; constructing an attenuation coefficient matrix according to the influence of the magnetization of the steel armor at each measuring point on the magnetic field distribution when there is no steel armor;

[0009] Step S2, assigning initial values ​​to unknown variables in the position coefficient matrix, the conductor current matrix and the attenuation coefficient matrix, and calculating the initial conductor current matrix and the initial attenuation coefficient matrix according to the initial variable values;

[0010] Step S3, according to the current variable values ​​of the unknown variables in the position coefficient matrix, the conductor current matrix and the attenuation coefficient matrix, the objective function value is calculated in combination with the measured sampling value matrix of the magnetic induction intensity component near the outer surface space of the multi-core cable; the calculated objective function value is compared with the first set judgment threshold value, if it is less than the first set judgment threshold value, the current variable value is substituted into the position coefficient matrix and the attenuation coefficient matrix to calculate the iterated position coefficient matrix and the attenuation coefficient matrix, and then enter step S4; if it is greater than or equal to the first set judgment threshold value, a random optimization algorithm is used to calculate a new variable that minimizes the objective function value, and then the objective function value is calculated according to the iterated new variable, and this step is repeated until the objective function value is less than the first set judgment threshold value, and then step S4 is entered;

[0011] Step S4, construct a linear equation system with the conductor current matrix as the unknown variable, and substitute the initial conductor current matrix and the initial attenuation coefficient matrix, solve the least squares solution of the linear equation system, and then solve the current iterative attenuation coefficient matrix according to the least squares solution, and then judge whether the ratio of the F-norm of the difference between the attenuation coefficient matrix calculated by the current iteration and the attenuation coefficient matrix calculated by the previous iteration and the F-norm of the attenuation coefficient matrix calculated by the previous iteration is less than or equal to the second set judgment threshold, if it is greater, return to step S3, otherwise record the final calculation results of the current attenuation coefficient matrix and the position coefficient matrix;

[0012] Step S5, substituting the final calculation results of the current attenuation coefficient matrix and the position coefficient matrix into the linear equations with the conductor current matrix as the unknown variable, when the sampling value of the magnetic induction intensity component is updated, solving the linear equations with the conductor current matrix as the unknown variable, and calculating the current value of each conductor of the current cable. When the present invention is implemented, the center surrounded by the multiple measurement points is the same as the center of the part to be measured. The random optimization algorithm adopted in step S3 of the present invention is realized by the existing random optimization algorithms such as gradient descent method, genetic algorithm, evolutionary algorithm, etc. The least square solution of solving the linear equations in step S4 of the present invention can be realized by applying regularization methods such as Moore-Penrose generalized inverse (SVD decomposition) and Tikhonov regularization.

[0013] Furthermore, the position coefficient matrix constructed in step S1 is represented as a position coefficient matrix P, whose element p ij represents the magnetic field component generated by the unit current at the j conductor position at the measuring point i, where the element p ij The calculation formula is as follows:

[0014]

[0015] In the formula, r i represents the radial coordinate of the measurement point i in polar coordinates, θ i Represents the angular coordinate of the measurement point i in polar coordinates, r' j represents the radial coordinate of the center of conductor j in polar coordinates, θ' j represents the angular coordinate of the center of conductor j in polar coordinates, μ 0 represents the vacuum magnetic permeability, j represents the conductor number in the multi-core cable, i represents the measurement point number; r i and θ i is a known quantity, r' j and θ' j Is an unknown quantity.

[0016] Further, the conductor current matrix constructed in step S1 is the conductor current matrix I c , which is expressed as:

[0017]

[0018] Where n represents the number of conductors in the multi-core cable, and N represents the total number of sampling points. Both n and N are known quantities.

[0019] Furthermore, the attenuation coefficient matrix constructed in step S1 is an attenuation coefficient matrix F, which is expressed as:

[0020] F = diag{f(J 1×n I c )}

[0021] The diag function converts the row vector into a diagonal matrix. 1×n is a row vector of all 1s, whose dimension is n, where n represents the number of conductors in a multi-core cable, I c is the conductor current matrix; f(J 1×n I c ) is a nonlinear function, representing a nonlinear mapping from matrix to matrix; x replaces the nonlinear function f(J 1×n I c ) 1×n I c , using the BH curve to approximate the function or To express the nonlinear function f(x) relationship, where a 1 、a 2 、a 3 is an unknown quantity and is a constant coefficient describing the f(x) curve.

[0022] Furthermore, in the specific implementation of step S2, it is first assumed that the current of each conductor of the multi-core cable has no harmonic components, and the equally spaced sampling values ​​of the current time domain waveform of a single conductor satisfy the following formula:

[0023]

[0024] Where A represents the amplitude of the current time domain waveform, represents the initial phase angle of the current time domain waveform, f represents the frequency of the current time domain waveform, and f s represents the sampling frequency of the current waveform during the test, N represents the total number of sampling points, and k represents the sampling point number; among them, A and are unknown quantities, f, f s and k is a known quantity;

[0025] Initial current matrix I c (0) It is expressed as:

[0026]

[0027] Among them, A t represents the amplitude of the current time domain waveform of conductor No. t, A represents the initial phase angle of the current time domain waveform of conductor No. t. t and All are unknown quantities, t = 1, 2, ..., n, n represents the number of conductors in the multi-core cable;

[0028] The unknown variables in the position coefficient matrix include the radial coordinates of the center of each conductor in the multi-core cable in polar coordinates r'={r' 1 ,r' 2 ,…,r' n}, and the angular coordinates of the center of each conductor in the multi-core cable in polar coordinates θ'={θ' 1 ,θ' 2 ,…,θ' n}; The unknown variables in the attenuation coefficient matrix include constant a={a 1 ,a 2 ,a 3};

[0029] For unknown variable r'={r' 1 ,r' 2 ,…,r' n}、θ'={θ' 1 ,θ' 2 ,…,θ' n}、A={A 1 ,A 2 ,…,A n}、 a={a 1 ,a 2 ,a 3}Assign initial value to get initial variable value Among them, the above unknown variables satisfy the following constraints when assigning initial values:

[0030] 0≤r′≤R c -R s

[0031] 0≤A≤A max

[0032]

[0033] 0≤θ≤2π

[0034]

[0035] In the formula, R c is a known quantity, representing the inner diameter of the cable armor; R s is a known quantity, representing the radius of the cable conductor; A max is the maximum value of the measured current amplitude;

[0036] In step S2, the initial variable value Initial current matrix I c (0) In the calculation, the initial conductor current matrix I c (0) The specific value of the initial conductor current matrix I c (0) Calculate the initial attenuation coefficient matrix F (0) Since the present invention calculates the current through the magnetic field measurement value, the sampling frequency f of the current waveform during the test s It is essentially the sampling frequency of the magnetic field waveform, which is defined according to different measurement requirements. The initial value setting in the present invention can be manually set based on experience, and if experience cannot be used, it can be set as a random value within the constraints.

[0037] Furthermore, the unknown variables in the position coefficient matrix include the radial coordinates of the center of each conductor in the multi-core cable in polar coordinates r'={r' 1 ,r' 2 ,…,r' n}, and the angular coordinates of the center of each conductor in the multi-core cable in polar coordinates θ'={θ' 1 ,θ' 2 ,…,θ' n}; The unknown variables in the conductor current matrix include the amplitude of the conductor current time domain waveform A = {A 1 ,A 2 ,…,An}, and the initial phase angle of the conductor current time domain waveform The unknown variables in the attenuation coefficient matrix include constant a={a 1 ,a 2 ,a 3}; where n represents the number of conductors in a multi-core cable;

[0038] In step S3, the current variable value Substitute into the objective function and calculate the function value. The objective function is:

[0039]

[0040] In the formula, ||M|| ∞ represents the L∞ norm of the matrix M, which is defined as the maximum value of the sum of the absolute values ​​of the elements in each row of the matrix, that is,

[0041]

[0042] B mea is the sample value matrix of the magnetic induction intensity component near the outer surface space of the multi-core cable measured, which is as follows:

[0043]

[0044] Where m is the total number of magnetic field measurement points and M refers to any matrix.

[0045] Furthermore, each conductor has 4 unknown variables to be solved, and the nonlinear function has 3 unknown variables to be solved, totaling 4n+3 unknown quantities. Each measuring point can list an equation, and the number of equations is the number of measuring points m. To ensure that the linear equation system has a least squares solution, the number of equations must be greater than the number of unknown quantities. The number of measuring points m and the number of conductors n set in step S1 satisfy the following condition: m>4n+3. In this way, the uniqueness and stability of the solution of the nonlinear equation system can be guaranteed.

[0046] Furthermore, in step S4, the calculation formula for judging whether the ratio of the F-norm of the difference between the attenuation coefficient matrix calculated in the current iteration and the attenuation coefficient matrix calculated in the previous iteration to the F-norm of the attenuation coefficient matrix calculated in the previous iteration is less than or equal to the second set judgment threshold is:

[0047]

[0048] In the formula, l is the number of iterations, F (l) is the attenuation coefficient matrix calculated for the current iteration, F (l-1) is the attenuation coefficient matrix calculated in the previous iteration; ε2 is the second set judgment threshold;

[0049] ||M||2 represents the F-norm of the matrix M, which is defined as the square root of the sum of the squares of all elements of the matrix, that is,

[0050]

[0051] n represents the number of conductors in the multi-core cable, m is the total number of magnetic field measurement points, ij is the element in the i-th row and j-th column of the matrix M. Further, the linear equation system constructed in step S4 with the conductor current matrix as the unknown variable is expressed as:

[0052] B mea =PI c F

[0053] Among them, P is the position coefficient matrix, I c is the conductor current matrix, F is the attenuation coefficient matrix, B mea It is the sample value matrix of the magnetic induction intensity component measured near the outer surface space of the multi-core cable.

[0054] In summary, compared with the prior art, the present invention has the following beneficial effects: compared with the finite element calculation method, the present invention does not need to perform complex grid division and differential equation solving, the complexity of the solution model is low, the amount of calculation and the requirements for running hardware are greatly reduced, and the measurement efficiency can be improved. Based on the time-invariant characteristics of the magnetization curve, the present invention uses a function to fit the nonlinear attenuation caused by the steel strip armor, and uses a random optimization algorithm to solve the undetermined coefficients. It does not need to obtain the BH curve data of the steel strip material in advance, and can perform adaptive calculations for the measured target, which can improve the measurement accuracy and is more universal. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, constitute a part of this application, and do not constitute a limitation of the embodiments of the present invention. In the drawings:

[0056] Figure 1 Schematic diagram of the structure of the steel belt armored multi-core power cable under test and the arrangement of magnetic field measurement points;

[0057] Figure 2 The flowchart of a specific embodiment of the present invention is shown in FIG. DETAILED DESCRIPTION

[0058] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with embodiments and drawings. The exemplary embodiments of the present invention and their description are only used to explain the present invention and are not intended to limit the present invention.

[0059] Example:

[0060] A current inversion method for a steel-belt armored multi-core cable comprises the following steps: step S1, setting a plurality of measurement points uniformly distributed along the circumference of the outer surface of the to-be-measured portion at the to-be-measured portion of the multi-core cable to be measured, establishing a polar coordinate system with the geometric center of the to-be-measured multi-core cable as the origin, constructing a position coefficient matrix according to the magnetic field measurement values ​​measured by the magnetic field sensor at the measurement points generated by the conductors in the to-be-measured multi-core cable; constructing a conductor current matrix by obtaining the current values ​​of each conductor of the multi-core cable at different times according to the current calculated from the magnetic field measurement values ​​at different times; constructing an attenuation coefficient matrix according to the influence of the magnetization of the steel armor at each measurement point on the magnetic field distribution when there is no steel armor; step S2, Initial values ​​are assigned to the unknown variables in the position coefficient matrix, the conductor current matrix and the attenuation coefficient matrix, and the initial conductor current matrix and the initial attenuation coefficient matrix are calculated based on the initial variable values; step S3, according to the current variable values ​​of the unknown variables in the position coefficient matrix, the conductor current matrix and the attenuation coefficient matrix, combined with the measured sampling value matrix of the magnetic induction intensity component near the outer surface space of the multi-core cable, the objective function value is calculated; the calculated objective function value is compared with the first set judgment threshold value, and if it is less than the first set judgment threshold value, the current variable value is substituted into the position coefficient matrix and the attenuation coefficient matrix to calculate the iterative position coefficient matrix and Attenuation coefficient matrix, and enter step S4; if it is greater than or equal to the first set judgment threshold, a random optimization algorithm is used to calculate a new variable that makes the objective function value obtain the minimum value, and then the objective function value is calculated according to the iterated new variable, and this step is repeated until the objective function value is less than the first set judgment threshold, and then enter step S4; step S4, construct a linear equation system with the conductor current matrix as the unknown variable, and substitute the initial conductor current matrix and the initial attenuation coefficient matrix, solve the least squares solution of the linear equation system, and then solve the current iterative attenuation coefficient matrix according to the least squares solution, and then judge the attenuation calculated by the current iteration. Whether the ratio of the F-norm of the difference between the subtraction coefficient matrix and the attenuation coefficient matrix calculated in the previous iteration to the F-norm of the attenuation coefficient matrix calculated in the previous iteration is less than or equal to the second set judgment threshold, if it is greater, return to step S3, otherwise record the final calculation results of the current attenuation coefficient matrix and the position coefficient matrix; step S5, substitute the final calculation results of the current attenuation coefficient matrix and the position coefficient matrix into the linear equation group with the conductor current matrix as the unknown variable, and when the sampling value of the magnetic induction intensity component is updated, solve the linear equation group with the conductor current matrix as the unknown variable to calculate the current current value of each conductor of the cable. Figure 1 As shown, in a specific implementation of the present invention, the center surrounded by the multiple measuring points is the same as the center of the part to be measured. Figure 1 The names corresponding to the figure marks are: 1. cable conductor, 2. insulation filling, 3. steel tape armor, 4. outer insulation sheath, 5. measuring point.

[0061] The specific implementation steps of this embodiment when applied to a model YJLV22-3×300 steel tape armored three-core cable are as follows: Figure 2 As shown, the specific steps include:

[0062] Step S1, setting a plurality of measurement points evenly distributed along the circumference of the outer surface of the multi-core cable to be tested at the tested part, establishing a polar coordinate system with the geometric center of the multi-core cable to be tested as the origin, and calculating the model definition. The calculation model definition in step S1 includes the following sub-steps:

[0063] Step S11, define the position coefficient matrix P, whose element p ij represents the magnetic field component generated by the unit current at the j conductor position at the measuring point i, where the element p ij Calculate according to formula (1):

[0064]

[0065] In the formula,

[0066] r i is a known quantity, representing the radial coordinate of the measuring point i in polar coordinates. In this embodiment, r i =45mm(i=1,2,…,24).

[0067] θ i is a known quantity, representing the angular coordinate of the measuring point i in polar coordinates. In this embodiment, θ i =(15×i)°(i=1,2,…,24).

[0068] r' j is an unknown quantity, representing the radial coordinate of the center of conductor j in polar coordinates. In this embodiment, j=1, 2, 3.

[0069] θ' j is an unknown quantity, representing the angular coordinate of the center of conductor j in polar coordinates.

[0070] μ 0 represents the vacuum magnetic permeability, j represents the conductor number in the multi-core cable, and i represents the measurement point number.

[0071] Step S12, define the conductor current matrix I c , represents the current value of each conductor of the cable at different times.

[0072]

[0073] in,

[0074] n is a known quantity, representing the number of cable conductors. In this embodiment, n=3.

[0075] N is a known quantity, representing the total number of sampling points. Since the current is calculated by the magnetic field measurement value, it is actually the total number of sampling points of the magnetic field waveform involved in the calculation. In this embodiment, N=160.

[0076] Step S13, define the attenuation coefficient matrix F as shown in formula (2).

[0077] F = diag{f(J 1×n I c )} (2)

[0078] In the formula,

[0079] F is the attenuation coefficient matrix, which represents the influence of the magnetization of the steel armor at each sampling point on the magnetic field distribution when there is no steel armor.

[0080] The diag function converts a row vector into a diagonal matrix.

[0081] J 1×n is a row vector of all ones with dimension n.

[0082] f(J 1×n I c ) is a nonlinear function, representing a nonlinear mapping from matrix to matrix.

[0083] Substituting x for the nonlinear function f(J 1×n I c ) 1×n I c In this embodiment, the function approximation of formula (3) is used.

[0084]

[0085] In the formula, a 1 、a 2 、a 3 is an unknown quantity and is a constant coefficient describing the f(x) curve.

[0086] Step S2, generating or calculating initial parameter values. Step S2 includes the following sub-steps:

[0087] Step S21, assuming that the current of each conductor of the cable has no harmonic components, the equally spaced sampling values ​​of the current time domain waveform of a single conductor satisfy formula (4).

[0088]

[0089] In the formula,

[0090] A is an unknown quantity, representing the amplitude of the current time domain waveform.

[0091] is an unknown quantity, representing the initial phase angle of the current time domain waveform.

[0092] f is a known quantity, representing the frequency of the current time domain waveform. In this embodiment, f=50 Hz.

[0093] f s It is a known quantity, representing the sampling frequency of the current waveform during the test. Since the current is calculated by the magnetic field measurement value, it is actually the sampling frequency of the magnetic field waveform. In this embodiment, it is 4kSPS, that is, 4000 points are collected per second.

[0094] k is a known quantity, representing the sampling point number.

[0095] Based on equation (4), the initial current matrix I c (0) It can be expressed as formula (5).

[0096]

[0097] in,

[0098] A t (t=1,2,3) is an unknown quantity, representing the amplitude of the current time domain waveform of conductor No. t.

[0099] It is an unknown quantity, representing the initial phase angle of the time domain waveform of the current in conductor No. t.

[0100] Step S22, for unknown variable r'={r' 1 ,r' 2 ,r' 3}、θ'={θ' 1 ,θ' 2 ,θ' 3}、A={A 1 ,A 2 ,A 3}、 a={a 1 ,a 2 ,a 3}Assign initial value to get initial variable value where r' (0) ={16,16,16},θ' (0) ={-30,90,210}, A (0) ={200,200,200}, a (0)) ={0.01,50,0.1}

[0101] The above variable values ​​should satisfy the inequality constraints as shown in formula (6).

[0102]

[0103] In the formula,

[0104] R c is a known quantity representing the inner diameter of the cable armor.

[0105] R s is a known quantity representing the radius of the cable conductor.

[0106] A max is the maximum value of the measured current amplitude.

[0107] A max It is the amplitude corresponding to the maximum value of the measured current, determined based on operating data or experience.

[0108] Step S23, initial variable value Substituting into equation (6), the initial conductor current matrix I is calculated c =I c (0) .

[0109] Step S24, the initial conductor current matrix I c (0) Substituting into equation (2), we can calculate the initial attenuation coefficient matrix F = F (0) .

[0110] Step S3, finding the local optimal solution of the attenuation coefficient matrix F by a random optimization method. Step S3 includes the following sub-steps:

[0111] Step S31: set the current variable value Substitute into the objective function of equation (8) and calculate the function value.

[0112]

[0113] In the formula,

[0114] ||M|| ∞ represents the L∞ norm of the matrix M, which is defined as the maximum value of the sum of the absolute values ​​of the elements in each row of the matrix, that is,

[0115]

[0116] Among them, m ij is the element in the i-th row and j-th column of the matrix M.

[0117] B mea is a known quantity, representing the sample value matrix of the tangential component of the magnetic induction intensity near the outer surface of the multi-core cable, as shown below.

[0118]

[0119] In this embodiment, the total number of magnetic field measurement points is 24.

[0120] Step S32, determine the objective function value g < ε 1 Is it true? If not, go to step S33; if true, then set the current variable value Substituting into equation (1) and equation (2), we can calculate the attenuation coefficient matrix F after iteration: *(0) and the position coefficient matrix P *(0) .

[0121] Among them, ε 1 is the first setting judgment threshold. In this embodiment, ε 1 =0.01.

[0122] Step S33, in this embodiment, an evolutionary algorithm called covariance matrix adaptive evolution strategy is applied to calculate a new variable that may minimize the value of formula (7) Return to step S31, substitute the iterated variables into equation (7) to calculate the objective function value until the judgment condition is met in step S32.

[0123] Step S4, construct a linear equation system to solve I c , iteratively optimize the attenuation coefficient matrix F. Step S4 includes the following sub-steps:

[0124] Step S41, construct I c is a linear equation system with unknown variables, as shown in formula (9), and substitute P = P *(0) 、F=F *(0) .

[0125] B mea =PI c F (9)

[0126] Step S42, finding the least squares solution I of the linear equation system of formula (9) c =I c (1) In this embodiment, Moore-Penrose generalized inverse (SVD decomposition) is applied to solve the equation to suppress the influence caused by the disturbance of the magnetic field sensor measurement.

[0127] Step S43, I c =I c (1) Substituting into formula (3), we can calculate F = F (1) .

[0128] Step S44, determine F (l) -F* (l-1) Whether the condition (11) is satisfied, if not, return to step S31 and set I c =I c (1) 、F=F(1) Substitute into the objective function of formula (7), and re-assign initial values ​​to the variables (r', θ', a), and iterate through the methods of step S32 and step S33 to calculate the attenuation coefficient matrix F after iteration *(l) and the position coefficient matrix P *(l) , then return to step S41; if established, record F *(l) , P *(l) These are the final calculation results of the attenuation coefficient matrix and the position coefficient matrix respectively.

[0129]

[0130] In the formula,

[0131] l is the number of iterations in step S4.

[0132] ε 2 is the second setting judgment threshold. In this embodiment, ε 2 =0.01.

[0133] ||M|| 2 represents the F-norm (Frobenius norm) of the matrix M, which is defined as the square root of the sum of the squares of all elements of the matrix, that is,

[0134]

[0135] Step S5, set F=F *(l) , P=P *(l) Substituting into equation (9), when the sampling value matrix B of the magnetic induction intensity component is mea After updating, solve the linear equation group (9) to calculate the current value I of each conductor of the cable c .

[0136] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A current inversion method for a steel tape armored multi-core cable, characterized in that: The following steps are involved: Step S1, setting a plurality of measurement points uniformly distributed along the circumference of the outer surface of the to-be-tested portion at the to-be-tested portion of the to-be-tested multi-core cable, establishing a polar coordinate system with the geometric center of the to-be-tested multi-core cable as the origin, constructing a position coefficient matrix according to the magnetic field measurement values ​​measured by the magnetic field sensor at the measurement points generated by the conductors in the to-be-tested multi-core cable; constructing a conductor current matrix according to the current calculated according to the magnetic field measurement values ​​at different times to obtain the current values ​​of each conductor of the multi-core cable at different times; The attenuation coefficient matrix is ​​constructed according to the influence of the magnetization of the steel armor at each measuring point on the magnetic field distribution when there is no steel armor; Step S2, assigning initial values ​​to unknown variables in the position coefficient matrix, the conductor current matrix and the attenuation coefficient matrix, and calculating the initial conductor current matrix and the initial attenuation coefficient matrix according to the initial variable values; Step S3, calculating the objective function value according to the current variable values ​​of the unknown variables in the position coefficient matrix, the conductor current matrix and the attenuation coefficient matrix, combined with the measured sampling value matrix of the magnetic induction intensity component near the outer surface space of the multi-core cable; The calculated objective function value is compared with the first set judgment threshold. If it is less than the first set judgment threshold, the current variable value is substituted into the position coefficient matrix and the attenuation coefficient matrix to calculate the iterative position coefficient matrix and the attenuation coefficient matrix, and then the process goes to step S4; if it is greater than or equal to the first set judgment threshold, a random optimization algorithm is used to calculate a new variable that makes the objective function value obtain the minimum value, and then the objective function value is calculated according to the iterative new variable, and this step is repeated until the objective function value is less than the first set judgment threshold, and then the process goes to step S4; Step S4, construct a linear equation system with the conductor current matrix as the unknown variable, and substitute the initial conductor current matrix and the initial attenuation coefficient matrix, solve the least squares solution of the linear equation system, and then solve the current iterative attenuation coefficient matrix according to the least squares solution, and then judge whether the ratio of the F-norm of the difference between the attenuation coefficient matrix calculated by the current iteration and the attenuation coefficient matrix calculated by the previous iteration and the F-norm of the attenuation coefficient matrix calculated by the previous iteration is less than or equal to the second set judgment threshold, if it is greater, return to step S3, otherwise record the final calculation results of the current attenuation coefficient matrix and the position coefficient matrix; Step S5, substitute the final calculation results of the current attenuation coefficient matrix and the position coefficient matrix into the linear equation group with the conductor current matrix as the unknown variable. When the sampling value of the magnetic induction intensity component is updated, solve the linear equation group with the conductor current matrix as the unknown variable to calculate the current current value of each conductor of the cable.

2. A current inversion method for a steel tape armored multi-core cable according to claim 1, characterized in that: The position coefficient matrix constructed in step S1 is represented as a position coefficient matrix P, whose element p ij represents the magnetic field component generated by the unit current at the j conductor position at the measuring point i, where the element p ij The calculation formula is as follows: In the formula, r i represents the radial coordinate of the measurement point i in polar coordinates, θ i Represents the angular coordinate of the measurement point i in polar coordinates, r' j represents the radial coordinate of the center of conductor j in polar coordinates, θ' j represents the angular coordinate of the center of conductor j in polar coordinates, μ0 represents the vacuum magnetic permeability, j represents the conductor number in the multi-core cable, and i represents the measurement point number; r i and θ i is a known quantity, r' j and θ' j Is an unknown quantity.

3. The current inversion method of a steel tape armored multi-core cable according to claim 1, characterized in that: The conductor current matrix constructed in step S1 is the conductor current matrix I c , which is expressed as: Where n represents the number of conductors in the multi-core cable, and N represents the total number of sampling points. Both n and N are known quantities.

4. The current inversion method of a steel tape armored multi-core cable according to claim 1, characterized in that: The attenuation coefficient matrix constructed in step S1 is an attenuation coefficient matrix F, which is expressed as: F=diag{f(J 1×n I c )} The diag function converts the row vector into a diagonal matrix. 1×n is a row vector of all 1s, whose dimension is n, where n represents the number of conductors in a multi-core cable, I c is the conductor current matrix; f(J 1×n I c ) is a nonlinear function, representing a nonlinear mapping from matrix to matrix; x replaces the nonlinear function f(J 1×n I c ) 1×n I c , using the BH curve to approximate the function or To express the nonlinear function f(x) relationship, where a1, a2, and a3 are unknown quantities and are constant coefficients describing the f(x) curve.

5. The current inversion method of a steel tape armored multi-core cable according to claim 1, characterized in that: In the specific implementation of step S2, it is first assumed that the current of each conductor of the multi-core cable has no harmonic components, and the equally spaced sampling values ​​of the current time domain waveform of a single conductor satisfy the following formula: Where A represents the amplitude of the current time domain waveform, represents the initial phase angle of the current time domain waveform, f represents the frequency of the current time domain waveform, and f s represents the sampling frequency of the current waveform during the test, N represents the total number of sampling points, and k represents the sampling point number; among them, A and are unknown quantities, f, f s and k is a known quantity; Initial current matrix I c (0) It is expressed as: Among them, A t represents the amplitude of the current time domain waveform of conductor No. t, A represents the initial phase angle of the current time domain waveform of conductor No. t. t and All are unknown quantities, t = 1, 2, ..., n, n represents the number of conductors in the multi-core cable; The unknown variables in the position coefficient matrix include the radial coordinates of the center of each conductor in the multi-core cable in polar coordinates r'={r'1, r'2, ..., r' n }, and the angular coordinates of the center of each conductor in the multi-core cable in polar coordinates θ'={θ'1,θ'2,…,θ' n }; The unknown variables in the attenuation coefficient matrix include constants a={a1, a2, a3}; For unknown variables r'={r'1,r'2,…,r' n }、θ'={θ'1,θ'2,…,θ' n }、A={A1,A2,…,A n }、 a={a1,a2,a3} assigns initial values ​​and obtains initial variable values Among them, the above unknown variables satisfy the following constraints when assigning initial values: 0≤r′≤R c -R s 0≤A≤A max 0≤θ≤2π In the formula, R c is a known quantity, representing the inner diameter of the cable armor; R s is a known quantity, representing the radius of the cable conductor; A max is the maximum value of the measured current amplitude; In step S2, the initial variable value Initial current matrix I c (0) In the calculation, the initial conductor current matrix I c (0) The specific value of the initial conductor current matrix I c (0) Calculate the initial attenuation coefficient matrix F (0) .

6. The current inversion method of a steel tape armored multi-core cable according to claim 1, characterized in that: The unknown variables in the position coefficient matrix include the radial coordinates of the center of each conductor in the multi-core cable in polar coordinates r'={r'1, r'2, ..., r' n }, and the angular coordinates of the center of each conductor in the multi-core cable in polar coordinates θ'={θ'1,θ'2,…,θ' n }; The unknown variables in the conductor current matrix include the amplitude of the conductor current time domain waveform A = {A1, A2, ..., A n }, and the initial phase angle of the conductor current time domain waveform The unknown variables in the attenuation coefficient matrix include constants a={a1, a2, a3}; wherein n represents the number of conductors in the multi-core cable; In step S3, the current variable value Substitute into the objective function and calculate the function value. The objective function is: In the formula, ||M|| ∞ represents the L∞ norm of the matrix M, which is defined as the maximum value of the sum of the absolute values ​​of the elements in each row of the matrix, that is, B mea is the sample value matrix of the magnetic induction intensity component near the outer surface space of the multi-core cable measured, which is as follows: Where m is the total number of magnetic field measurement points.

7. A current inversion method for a steel tape armored multi-core cable according to claim 6, characterized in that: The number of measurement points m and the number of conductors n set in step S1 satisfy the following condition: m>4n+3.

8. The current inversion method of a steel tape armored multi-core cable according to claim 1, characterized in that: The calculation formula for judging whether the ratio of the F-norm of the difference between the attenuation coefficient matrix calculated in the current iteration and the attenuation coefficient matrix calculated in the previous iteration to the F-norm of the attenuation coefficient matrix calculated in the previous iteration is less than or equal to the second set judgment threshold in step S4 is: In the formula, l is the number of iterations, F (l) is the attenuation coefficient matrix calculated for the current iteration, F (l-1) is the attenuation coefficient matrix calculated in the previous iteration; ε2 is the second set judgment threshold; ||M||2 represents the F-norm of the matrix M, which is defined as the square root of the sum of the squares of all elements of the matrix, that is, n represents the number of conductors in the multi-core cable, m is the total number of magnetic field measurement points, ij is the element in the i-th row and j-th column of the matrix M.

9. A current inversion method for a steel tape armored multi-core cable according to any one of claims 1 to 8, characterized in that: The linear equation system constructed in step S4 with the conductor current matrix as the unknown variable is expressed as: B mea =PI c F Among them, P is the position coefficient matrix, I c is the conductor current matrix, F is the attenuation coefficient matrix, B mea It is the sample value matrix of the magnetic induction intensity component measured near the outer surface space of the multi-core cable.

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